HS-125 Captain reported encountering wake turbulence in trail of a C-130 in SCT airspace.

Narrative

We were level at 15;000 feet and instructed to climb to a higher altitude. Both myself and the First Officer had been observing traffic on our TCAS indicating 500 feet above us and at our 12 o'clock position that appeared to be heading towards us and 4 miles in range and closing that they had not called out to us. I informed ATC of the traffic and that we did not want to climb. There were numerous other aircraft on the frequency stepping on each other which made communication poor while the situation was unfolding. In the meantime we hit turbulence which rolled the aircraft about 30 degrees in bank to the left and about 3-5 degrees down. I disconnected the auto pilot and took control from the First Officer who was flying at the time. In the recovery period; I gained about 400 feet of altitude before things got settled down. We were instructed to fly heading and altitude at that point by the controller who was being repeatedly stepped on in transmissions between both of us. The other aircraft ended up being a C-130 and we had flown into his wake as he was headed the same direction we were. Because of our higher airspeed than his; it had appeared to us that he was coming towards us in the opposite direction until we were able to visually see that we were overtaking him instead. Separation was maintained and the altitude and heading was adhered to after things settled down. SoCal shortly afterward handed us off to LA Center and I advised them of our running thru the C-130's wake which had led to our deviations. The controller acknowledged she was sorry and we continued our flight uneventful from there. Too much traffic on the frequency certainly contributed to communication problems thru the incident.